Đáp án: + Giải thích các bước giải:
$a$) `(-2/3)^2 . (2 1/2 - 3 3/4) - 1 1/2 : (-0,84 + 1/{25}) - {2^2}/{3^2}`
`= 4/9 . (5/2 - {15}/4) - 3/2 : ({-21}/{25} + 1/{25}) - 4/9`
`= 4/9 . (-5/4) - 3/2 : (-4/5) - 4/9`
`= -5/9 + {15}/8 - 4/9`
`= -1 + {15}/8`
`= 7/8`.
$b$) `(14,75 - 15 5/6 ) : 3 1/4 - (5/8 - {18}/{27} + 9/{54}) : (- 3/4)^2 + \sqrt{{25}/{16}}`
`= ({59}/4 - {95}/6) : {13}/4 - (5/8 - 2/3 + 1/6) : 9/{16} + 5/4`
`= {-13}/{12} . 4/{13} - 1/8 . {16}/9 + 5/4`
`= -1/3 - 2/9 + 5/4`
`= {25}/{36}`.
$c$) `[(-2/3)^2 + 0,75]. 3 3/5 - \sqrt{{36}/{25}} : (-1 4/5)`
`= (4/9 + 3/4) . {18}/5 - 6/5 : (-9/5)`
`= {43}/{36} . {18}/5 + 6/5 . 5/9`
`= {43}/{10} + 2/3`
`= {149}/{30}`.
$d$) `2^3 + 3 . (1/2)^0 - (-2)^2 . 4 + ( -2^2 : \sqrt{1/4}) . 8`
`= 8 + 3.1 - 4.4 + (-4 : 1/2) . 8`
`= 8 +3 - 16 - 8.8`
`= -5 - 64`
`= -69`.
$e$) `\sqrt{0,49} . \sqrt{{16}/{25}} + \sqrt{4/{81}} : \sqrt{{25}/{81}} - (- 1/2)^3`
`= 7/{10} . 4/5 + 2/9 : 5/9 + 1/8`
`= {14}/{25} + 2/5 + 1/8`
`= {217}/{200}`.
$f$) `(-2/3)^3 - 3(-3/2)^2 - 2(-3/2)^{-1} + 4.(- 1/{201})^0`
`= - 8/{27} - 3. 9/4 - 2 . {-2}/3 + 4.1`
`= - 8/{27} - {27}/4 + 4/3 + 4`
`=- {185}/{108}`.
$g$) `{4^6 . 9^5 + 6^9 . 120}/{-6^{11} - 8^4 . 3^{12}}`
`= {(2^2)^6 . (3^2)^5 + (3.2)^9 . 2^3 . 3.5}/{-[(2.3)^{11} + (2^3)^4 . 3^{12}]}`
`= {2^{12} . 3^{10} + 3^9 . 2^9 . 2^3 . 3 . 5}/{-(2^{11} . 3^{11} + 2^{12} . 3^{12})}`
`= {2^{12} . 3^{10} + 3^{10} . 2^{12} . 5}/{-(2^{11} . 3^{11} + 2^{12} . 3^{12})}`
`= {2^{12} . 3^{10} . (1 + 5)}/{-2^{11}.3^{11} . (1 + 2.3)}`
`= {2 . 6}/{-3.7}`
`= -4/7`.
